I. Field of the invention
The present invention relates to gyroscopes.
More particularly, the present invention incorporates a stationary three-fold symmetric vibratory rate gyroscope implementation provided on a thick-film silicon-on-insulator (SOI), micro electro-mechanical system (MEMS).
II. Discussion of the Background
Small, affordable, and reliable inertial components are required for small diameter precision-guided military weapon systems. Gyroscopes are inertial components or devices that can sense angular rotation and/or rotation rate. The ring laser and interferometric fiber optic gyroscopes dominate the current tactical missile system market. Although these gyroscope technologies meet most inertial requirements, they tend to be moderately expensive. Recent advancements in microelectromechanical systems (MEMS) technologies make it possible to develop miniaturized, low cost angular rate sensors. The process technologies initially developed for fabricating integrated circuits have now evolved to allow development of MEMS devices.
Although many organizations are developing MEMS gyroscopes for a variety of applications, most do not begin to address the demanding and challenging requirements for military combat systems. Requirements for small precision guided weapons were the basis for the MEMS gyroscope development criteria. Rate sensing in many small diameter missile guidance units typically requires a rate resolution of 10°/hr. Additionally, for a particular guided munition, a large roll rate about its longitudinal axis may be experienced during flight. The anticipated rotational rates encompass a range of −3000° to +3000°/sec, resulting in a dynamic range of 107.
In order to control the heading of this system during flight, the system must know its roll angle about the longitudinal axis so that the control systems can adjust accordingly. Therefore, the accuracy of this angular measurement must correspond to a bias stability of 10°/hr in order for the guidance system to compensate.
Furthermore, actuators in the control system of the guided munition may result in a substantial vibration environment. Large shocks of greater than 1000 G's can be seen at frequencies ranging from 5 kHz to 15 kHz. Additionally, the inertial device must operate through military temperature environments (−55° to +125°). The criteria for achieving superior resolution while measuring large rotation rate adds difficulty to design determination since there are tradeoffs that exist in determining the mechanical structure's topology.
For example, achieving superior resolution requires substantial inertial mass available in the device. However, when a large mass design is devised, the resulting deflections due to large values of rotational rate are generally more than the device can accommodate. In most cases, enough electrostatic feedback force cannot be produced to counter the Coriolis forces. Given that the MEMS gyroscope must not only survive but operate through these harsh environments, the challenge has been to develop a robust, accurate and reliable MEMS gyroscope.
MEMS angular rate sensors or gyroscopes that detect angular rate utilize the Coriolis Effect. A vibratory rate gyroscope is a sensor that detects and measures rotation by generating and measuring Coriolis acceleration. In other words, the sensing method used in a vibratory rate gyroscope is based on the Coriolis pseudo-force resulting from a translating body in a rotating frame of reference. The conventional illustrations of FIG. 1 and FIG. 2 demonstrate the Coriolis Effect on an object.
A mass, m, is moving at time, t, with a velocity vx along both the (x,y) and (x′,y′) axes.
At time t+dt, the (x′,y′) axes have rotated Ωdt where Ω is the rotational rate. In accordance with Newton's Laws, the mass is still moving with velocity vx in the (x,y) frame of reference.
However, in the (x′,y′) frame of reference, is appears that the velocity, vx has moved by an amount dvx. Therefore the Coriolis acceleration and force is:
                    α        =                                            ⅆ              v                                      ⅆ              t                                =                                    -              2                        ⁢                                                  ⁢            Ω            ⁢                                                  ⁢                          v              x                                                          Equation        ⁢                                  ⁢                  (          1          )                    F=ma=−2mΩvx   Equation (2)
The fundamental result from this simple derivation of system dynamics is that a translating mass in a rotational frame of reference will appear to experience, within the rotating frame, a force orthogonal to its velocity and proportional to its velocity and the rate of rotation of that frame of reference.
The conventional vibratory rate gyroscope consists of a mass-spring system that has at least two orthogonal modes of oscillation (FIG. 3). The mass is forced to have an oscillatory velocity in the frame of reference of the device along the x-axis. Anchored springs 16 and 14 having respective identical spring constants kx and ky are attached to respective rollers 20 and 18 so as to provide a suspension that constrains the mass to particular orthogonal oscillation modes. When the device experiences rotation, the Coriolis force induces oscillation of the orthogonal mode of the device. Sensors detect this motion and provide a signal from which the rotational rate is extracted. The Coriolis force is proportional to the external rotation rate.
The equations of motion for a mass-spring system moving in a non-inertial reference frame are found using Lagrangian dynamics. Expressions for the potential energy and kinetic energy of the system must be derived first.
The global frame of reference is the p-q-a frame, the local frame of reference x-y-φ is rotated by an angle θ with respect to the global frame. The local frame is also translated by rx and ry with respect to the global frame.
The potential energy stored in the springs is:
                    PE        =                                            1              2                        ⁢                          k              x                        ⁢                          x              2                                +                                    1              2                        ⁢                          k              y                        ⁢                          y              2                                +                                    1              2                        ⁢                          k                              ϕ                ⁢                                                                                        ⁢                          ϕ              2                                                          Equation        ⁢                                  ⁢                  (          3          )                    
The kinetic energy is calculated in the global frame of reference, using the global variables:
                    KE        =                                            1              2                        ⁢                                          m                ⁡                                  (                                                            ⅆ                      q                                                              ⅆ                      t                                                        )                                            2                                =                                                    1                2                            ⁢                                                m                  ⁡                                      (                                                                  ⅆ                        p                                                                    ⅆ                        t                                                              )                                                  2                                      +                                          1                2                            ⁢                                                I                  ⁡                                      (                                                                  ⅆ                        α                                                                    ⅆ                        t                                                              )                                                  2                                                                        Equation        ⁢                                  ⁢                  (          4          )                    
The global variables are related to variables in the local frame of reference by rotation matrices:q(t)=cos(θ)x(t)−sin(θ)y(t)+rx(t)   Equation (5)p(t)=sin(θ)x(t)+cos(θ)y(t)+ry(t)   Equation (6)i a(t)=θ(t)+φ(t)   Equation (7)
The equations of motion in the local frame of reference are found from
                              F                      x            i                          =                                            ∂              L                                      ∂                              x                i                                              -                                    ⅆ                              ∂                L                                                                    ⅆ                t                            ⁢                              ∂                                  x                  i                                                                                        Equation        ⁢                                  ⁢                  (          8          )                    
Where xi are generalized coordinates, Fx, are external forces such as damping and excitation forces, and L is the Lagrangian (L=KE−PE).
The global coordinates in the kinetic energy relation are substituted by Equations (5), (6) and (7) to convert to local coordinates. Equation (8) is then applied for each of the on-chip coordinates (x, y, φ), by replacing the generalized coordinate by the respective on-chip coordinate, yielding:
                                             x            ¨                    =                                                    -                                  ω                  x                  2                                            ⁢              x                        -                                                            ω                  x                                Q                            ⁢                              x                .                                      -                                          F                x                            m                        +                          x              ⁢                                                          ⁢                              Ω                2                                      +                          y              ⁢                                                          ⁢                              Ω                .                                      +                          2              ⁢                                                          ⁢              Ω              ⁢                                                          ⁢                              y                .                                      -                                          a                x                            ⁢              cos              ⁢                                                          ⁢              θ                        -                                          a                y                            ⁢              sin              ⁢                                                          ⁢              θ                                                            Equation          ⁢                                          ⁢                      (            9            )                                                                    y            ¨                    =                                                    -                                  ω                  y                  2                                            ⁢              y                        -                                                            ω                  y                                Q                            ⁢                              y                .                                      -                          2              ⁢                                                          ⁢              Ω              ⁢                                                          ⁢                              x                .                                      +                          y              ⁢                                                          ⁢                              Ω                2                                      -                          x              ⁢                                                          ⁢                              Ω                .                                      +                                          a                x                            ⁢              sin              ⁢                                                          ⁢              θ                        -                                          a                y                            ⁢              cos              ⁢                                                          ⁢              θ                                                            Equation          ⁢                                          ⁢                      (            10            )                                                                    I            ⁢                                                  ⁢                          ϕ              ¨                                =                                                    -                                  k                  ϕ                                            ⁢                              ϕ                .                                      -                          I              ⁢                                                          ⁢              ϕ                                                            Equation          ⁢                                          ⁢                      (            11            )                              
Where wx2=kx/m and wy2=ky/m are the resonant frequencies of the x and y modes, respectively, ax and ay are external accelerations, and Q is the quality factor of resonance. The Coriolis accelerations are the 2Ω{dot over (y)} and 2Ω{dot over (x)} terms. The last two terms in Equations (9) and (10) are the acceleration terms, which create transients at the natural frequency of the system. The terms yΩ and xΩ refer to the inertia of angular acceleration. The terms yΩ2 and xΩ2 are centripetal accelerations, and act as spring softeners.
The importance of the above derivation is that it includes extra terms in the equations of motion beyond the standard Coriolis force terms. When experiencing large rotational rates and angular accelerations, these extra terms, the centripetal acceleration, linear acceleration and angular accelerations, play larger roles in the error terms of the rotational rate signal.
In addition, the derivation shows, as is commonly known, the role of matching resonant frequencies so that the benefits of a high quality factor can be applied to the sensor.
The coefficients in the above equations, particularly the spring constant and quality factor, are dependent on temperature. In prior art systems, the temperature sensors are prone to sense temperatures at variance from the actual temperature of the gyroscope. Such a result causes errors in the rotational calculations.
In micro-electronic designs, the proof mass of the gyrroscope is positioned and moves above a base substrate surface. Even when experiencing high G forces, the proof mass must remain above the substrate surface.